Question

Assume that adults have iq scores that are normally distributed with a mean of 100 and a standard deviation of 20. if all iq scores are converted to z-scores, what would the mean and standard deviation of all z scores be

Answer 1

Let X be the iq score of adults. X is normally distributed with mean of 100 and standard deviation of 20.

If all iq scores are converted to z -scores then we will get z scores. And the z score is standard normal variable with mean=0 and standard deviation =1

Hence the mean and standard deviation of of all z scores will be 0 and 1 respectively.